1 Introduction

Worldwide, lung cancer is the leading cause of cancer deaths in men, whereas breast cancer is the leading cause of cancer deaths in women [1, 2]. To understand the molecular biology of cancer, we have to be able to identify and understand the underlying mutations. The most frequently altered gene in human cancers is TP53, which is either directly inactivated by somatic mutations in about 50% of these human cancers or indirectly inactivated in the remainder through binding to viral proteins or having impaired pathways [3, 4].

The p53 protein functions primarily as a transcription factor that can either activate or repress the expression of a large number of DNAs and microRNAs [5, 6] and as a mediator for integrating appropriate cellular signals via protein–protein and protein–DNA interactions [7]. When the p53 protein fails to function properly, uncontrolled growth and division of cells arises causing genomic instability, a sign of cancer [4]. Therefore, the p53 protein is essential for preventing cancer development via complicated interactions, which are mediated by p53 independently folded and fundamentally disordered functional domains [8].

The monomeric form of the p53 protein consists of 393 amino acid residues and has a modular domain structure consisting of three major functional domains: the N-terminal domain (NTD), which functions mainly as a transcription-activation domain [8], the core domain, which functions as a sequence-specific DNA binding domain (DBD) [9], and the C-terminal domain (CTD), which functions as a modulator for the transcriptional activity of p53 protein and as a binding domain to different target proteins or nonspecific DNA [8].

The boundaries of the major p53 domains and their subdomains are demonstrated in Fig. 1 according to the discovered p53 isoforms and the pinpointed structural-functional features of human p53 protein [8, 10,11,12,13,14,15,16,17,18]. The p53-NTD, spanning residues (1–93) [8], contains 3 subdomains: the transcription-activation domain 1 (TAD\(_{1}\)), spanning residues (1–39) [11, 14], the transcription-activation domain 2 (TAD\(_{2}\)), spanning residues (40–60) [8], and the proline-rich domain (PRD), spanning residues (64–93) [8]. The p53-DBD has spanning residues (94–292) [18]. The p53-CTD, spanning residues (293–393) [8], contains 2 subdomains: the oligomerization domain (OD), spanning residues (325–356) [10], and the regulatory domain (RD), spanning residues (358–393) [12, 13, 15,16,17].

Fig. 1
figure 1

3D structure of full-length wild-type p53 model. Colors show domains and subdomains: blue, transcription-activation domain 1 (TAD\(_{1}\)); azure, transcription-activation domain 2 (TAD\(_{2}\)); magenta, proline-rich domain (PRD); green, DNA binding domain (DBD); gray, flexible linker; orange, oligomerization domain (OD); red, regulatory domain (RD). The Arg175 is depicted with CPK representation. This model refers to the equilibrated distal-active p53 conformation (Color figure online).

Full size image

It is known that a biologically active form of the human p53 protein is formed by a homotetramer comprising four identical chains [5]. Accordingly, a model of full-length p53 bound to DNA has been proposed [19]. In the proposed model, two p53-RD units are far from the DNA (distal p53-RD) and the other two are close to the DNA (proximal p53-RD). In a cryo-electron microscopy study [20], the relative arrangement of p53-OD and p53-DBD structures has been revealed; consequently, this orientation facilitates modeling of the natively folded domains.

The full-length structure of a wild-type human p53 protein is not only crucial for understanding the role of p53 protein in the cell cycle and in other activities, but also it is necessary in the design of drugs that target mutant forms of the p53 protein [5]. In breast cancer, the top five substitution mutations in the p53 protein with their frequencies are Arg175His (185), Arg248Gln (156), Arg273His (141), Arg248Trp (122), and Arg273Cys (74) [21]. The Arg175His mutant is one of the designated hotspot mutations in the p53 protein, and the hotspot mutations of Arg175 are classified as conformational mutants, which fail to stabilize the \({\beta }\) sandwich in the human p53-DBD; consequently, these mutants lack the appropriate scaffold for the proper interaction with DNA [8]. In addition, the Arg175His mutant perturbs the zinc-binding region, which causes structural instability, rapid exchange between folded and unfolded states, and hydrophobic aggregation at physiological temperature [8, 22, 23].

The ability of the p53 protein to prevent cell proliferation (i.e., suppressing tumor development) is considered a promising therapeutic goal, which can be achieved through the induction of an irreversible exit from the cell cycle or activation of cell death [6]. Small molecules and elimination of mutant p53 are among the approaches that have been adopted in p53-based cancer therapies [4, 24]. The p53-targeted therapies are considered attractive cancer therapies; however, the p53 protein is still a challenging target for drug discovery because p53 does not offer the accessibility of a receptor-ligand interaction or an enzyme active site; thus, there are challenges in the development of p53-targeted therapy [4, 25].

Gaussian accelerated molecular dynamics (GaMD) facilitates unconstrained-enhanced sampling of a biomolecular system by adding a harmonic boost potential to smooth the system’s potential energy surface [26]. Relative to the classical molecular dynamics (MD) simulations, the GaMD simulations demonstrate acceleration of biomolecular kinetics [27]. The novel GaMD method has several applications in sampling biomolecular systems and free-energy calculations of biomolecules, such as, predicting drug-receptor interactions [28], deciphering the mechanism of the G-protein-coupled receptors and the G protein interactions [29], and predicting the interactions between the G-protein-coupled receptors and the membrane lipids [30].

All together, the full-length human p53 proteins, wild-type and Arg175His mutant forms, can be used as reference systems in comparing the GaMD results versus the classical MD results. Therefore, in this study we have built p53 forms by utilizing the relative orientation of p53-OD to p53-DBD [20]; thus, enhancing the credibility and realisticity of our forms to be solvated with an OPC water model and be studied by GaMD technique at physiological temperature and pH. In addition, the principal component analysis (PCA) technique has been applied on the GaMD results, and the most probable druggable pockets in the Arg175His mutant forms have been predicted.

2 Methods

2.1 Molecular Modeling

The starting structures of the wild-type p53-DBD forms were taken from chain B of PDB entry 2OCJ [31], an inactive (DNA-free) structure, and from chain A of PDB entry 4HJE [32], an active structure. An initial structure for a wild-type p53-OD form was chosen from the first conformer of chain D of PDB entry 3SAK [33]. In the next three paragraphs, the modeling steps were done using UCSF Chimera [34], version 1.15, and its built in Modeller, version 9.23, functions [35].

The two PDB structures of p53-DBD were superposed along with the PDB structure of p53-OD on a Cryo-EM structure, the PDB entry 5XZC [20], using \(\text {C}_{\alpha }\) atoms. Superposition on chain B of PDB entry 5XZC generated two models, inactive and proximal-active models, whereas superposition on chain C of PDB entry 5XZC generated distal-active model. After the superposition process, a flexible loop (FL) between a p53-DBD and the p53-OD structures was modeled. Because of the natural disordered state of human p53-TAD, p53-PRD, and p53-RD [5], these parts were modeled at Robetta web server [36, 37], a de novo protein-structure-prediction server. The generated p53-TAD, p53-PRD, and p53-RD models were superposed on each p53-DBD–p53-OD model using \(\text {C}_{\alpha }\) atoms. Loop refinement was applied on each model; thus, three full-length p53 forms were obtained, namely, inactive, distal-active, and proximal-active p53 forms.

Two mutant forms were generated using wild-type distal-active and proximal-active p53 forms. The mutation process, mutating Arg175 residue to His175 residue, was achieved with the pdb4amber program in Amber 20 [38,39,40]. To remove residue–residue clashes because of the mutation process, minimization in vacuum was applied on each mutant. The minimization process consisted of 50 cycles; 20 cycles of steepest-descent energy minimization process followed by 30 cycles of conjugate-gradient energy minimization process.

To fulfill the physiological pH condition (i.e., \(\text {pH}\, 7.4\)) [41] in each full-length p53 form, Asp and Glu residues were deprotonated, Arg and Lys residues were protonated, and His residues kept neutral. To model the coordinated \(\text {Zn}^{2+}\) complex state [42], three Cys residues were deprotonated (i.e., Cys176, Cys238, and Cys242 were assigned a \(-1\) charge). This zinc model, with the protonation state of \(-1\), was found to be the only model that kept the zinc interface structure intact (i.e., maintaining the tetrahedral structure) [42]. The detailed atomic charge calculations for the amino acids residues in the zinc model, using B3LYP density functional method with the 6-311+G** basis set, were reported [42]. Both N- and C-termini of each full-length p53 form were capped with acetyl (ACE) and N-methyl (NME) groups, respectively to keep them neutral. The ACE and NME groups were obtained from RCSB Protein Data Bank [43, 44].

The LEaP module of Amber 20 [38,39,40] was used for adding missing atoms, applying ff14SB protein force field [45], solvating the protein in a truncated octahedron box of OPC water molecules [46] with a buffering distance set to \(12.0~{\AA }\), loading Li/Merz ion parameters (12–6–4 set) for monovalent [47] and \(+2\) [48] ions in the designated water model, and neutralizing the modeled system with charge neutralizing counter ions (i.e., \(\text {Na}^{+}\) ions). The Li/Merz ion parameters were selected because they were designed for the monovalent, divalent, trivalent, and tetravalent ions [38,39,40]; that is, the same force field was used for all ions. Unlike the widely used TIP3P water model [49], the OPC water model was recommended to be used with ff14SB protein force field in biomolecular simulations [40]. Combining OPC water model with ff14SB protein force field in MD simulations has improved the accuracy of atomistic simulations and given better modeling sequence-specific behavior, protein mutations, and rational protein-design results [50].

2.2 GaMD Simulations

Gaussian accelerated molecular dynamics simulations were performed using PMEMD engine within the Amber 20 software suite [38,39,40]. The total preparation simulation time for each system with positional and distant restraints was \(11.5~\text {ns}\) (Table 1). In Table 1, system preparation protocol included several conjugate-gradient energy minimization processes, heating from 0 to 310.15 K, and several equilibration processes at different periodic boundary conditions.

Table 1 Summary of system preparation protocol for active and mutant forms
Full size table

The applied position restraints were relative to the initial coordinates of the modeled system. In the DNA-free form and at \(300~\text {K}\) [51], it was observed that the \(\text {Zn}^{2+}\) binding site did not have a stable structure; the spontaneous \(\text {Zn}^{2+}\) release leads to dissociation of His179 from \(\text {Zn}^{2+}\); thus, increasing the thermal fluctuation of L2 loop. Therefore and to maintain four-ligand coordinations of zinc in the protein at physiological temperature and during long-time simulations, the distance restraint approach was chosen [42, 52], but the bond lengths were selected relative to the bond lengths in the PDB structure of the modeled system, and the force constant parameters were interpolated from the zinc Amber force field data [53]. For active and mutant forms, the utilized force constant for Cys-SG-Zn bond was \(56.36~\text {kcal/}(\text {mol}\cdot{\AA }^{2})\), and for His-ND1-Zn bond was \(51.53~\text {kcal/}(\text {mol}\cdot{\AA }^{2})\). For inactive form, the utilized force constant for Cys-SG-Zn bond was \(25.93~\text {kcal/}(\text {mol}\cdot{\AA }^{2})\), and for His-ND1-Zn bond was \(58.98~\text {kcal/}(\text {mol}\cdot{\AA }^{2})\).

The temperature was maintained at physiological value of \(310.15~\text {K}\) using Langevin dynamics [54] with a collision frequency of \(5~\text {ps}^{-1}\). The pressure was maintained at \(1~\text {bar}\) with isotropic position scaling using Berendsen barostat [55] with pressure relaxation time of \(1~\text {ps}\). The nonbonded cutoff was assigned to \(9.0~{\AA }\). The Particle Mesh Ewald method [56] with its default parameters was used to calculate the full electrostatic energy of the unit cell in a macroscopic lattice of repeating images. The SHAKE algorithm [57] was used in all simulation processes, but not in minimization processes, to constrain hydrogen atoms. Consequently, the time step was assigned to \(2~\text {fs}\) for dynamics integration except at specific processes mentioned in Table 1, where it was assigned to \(1~\text {fs}\) to maintain system stability.

In Table 1, the last equilibration process was necessary for conducting the GaMD simulation [26]. A dual boost on both dihedral and total potentials was applied on the last equilibration process and production runs. The last equilibration process involved 4 stages: \(2.0~\text {ns}\) of preparatory stage as conventional MD (no statistics were collected), \(3.0~\text {ns}\) of initial stage as conventional MD (potential statistics were calculated for GaMD pre-equilibration stage), \(2.0~\text {ns}\) of GaMD pre-equilibration stage as preparation biasing MD simulation (boost potential was applied but boost parameters were not updated), and \(3.0~\text {ns}\) of GaMD equilibration stage as biasing MD simulation (boost potential was applied and boost parameters were updated). The average and standard deviation of potential energies were calculated every \(0.5~\text {ns}\), and the rest of GaMD parameters were assigned their default values. To enhance sampling simulations and free energy calculation of biomolecules, GaMD was applied on each system for a simulation time of \(200~\text {ns}\). The GaMD production trajectory files were written every \(2.0~\text {ps}\).

2.3 Data Analysis

R language [58], version 3.6.3, python language [59], version 3.7.3, cpptraj [60], version 4.25.6, and pytraj [60], version 2.0.6, were used for composing analysis scripts and for generating analysis figures. Analysis scripts included root-mean-square displacement (RMSD), root-mean-square fluctuation (RMSF), radius of gyration, PCA, clustering, and free-energy profiles.

2.3.1 Root-Mean-Square Deviation

RMSD reflects the degree of similarity between three-dimensional protein structures. It can be computed [61,62,63] by measuring the RMSD between backbone atoms of superimposed protein structures (the protein structure in trajectory frame i and the restart frame from the last equilibration process).

2.3.2 Root-Mean-Square Fluctuation

RMSF reveals the conformational variance of the protein. It can be measured [61,62,63] by calculating the deviation between the position of atom i (usually \(\text {C}_{\alpha }\)) with respect to its average position over the whole simulation trajectory.

2.3.3 Radius of Gyration

In biological molecules, radius of gyration indicates the protein structure compactness [64]. It can be determined [61,62,63] by measuring the root mean square distance from protein atoms (usually \(\text {C}_{\alpha }\)) to their center of mass. Among the major protein classes (i.e., \({\alpha }\), \({\beta }\), \({{\alpha } / {\beta }}\), and \({{\alpha } + {\beta }}\)) and when protein size is larger than 300 amino acid residues, \({\alpha }\) proteins have the highest radius of gyration indicating the least tight packing character as compared with the character of other classes, whereas \({{\alpha } / {\beta }}\) proteins have the lowest radius of gyration indicating the tightest packing character as compared with the character of other classes [64]. Maintaining a relatively steady value of radius of gyration over time reveals the stability of the protein folding state.

2.3.4 Principal Component Analysis

Conducting PCA reveals the most important motions of a biological system over a broad range of time and spatial scales [65]. PCA is a multivariate statistical technique that reduces the number of dependent motions needed to describe the dynamics of a biological system into a smaller number of independent motions called principal components [65]. The first principal component, the eigenvector with the highest corresponding eigenvalue, reflects the most identifying motion patterns in the simulation [65]. The eigenvalues show the contribution of the corresponding eigenvectors to the global fluctuations of a biological system.

In our GaMD simulations, PCA was performed [61,62,63] on all heavy atoms of the protein after removing all global translations and rotations about the center of mass and orienting all structures with respect to the restart frame from the last equilibration process. The porcupine plots were generated using the porcupine plot plugin in VMD [66].

2.3.5 Clustering Analysis

Clustering analysis is a technique that finds patterns within data by locating clusters of geometrically similar conformers in ensembles of chemical conformations [67]. Most clustering algorithms measure distance between objects to compute the dissimilarity matrix; thus, clustering algorithms can be divided into partitional and hierarchical clustering methods.

In this study, k-means clustering method [61,62,63] has been used because of its one of the fastest and most widely used techniques, and it has apparent good performance in analyzing MD trajectory data [67]. The k-means clustering method aims at dividing n observations into non-overlapping k clusters in which each observation belongs to the cluster with the closest centroid, and each centroid depicts the conformation that best represents the conformations within a cluster [67]. The quality of a k-means partition is evaluated by calculating the percentage as indicated by Eq. 1 [67], where BSS stands for between sum of squares, TSS stands for total sum of squares, and CQ stands for cluster quality.

$$\begin{aligned} CQ ~=~ \dfrac{BSS}{TSS} \times 100\% \end{aligned}$$
(1)

The higher the percentage, the better the score (and thus the quality). Thus, the optimal number of clusters for a k-means approach has been determined by NbClust function [68] built in R language [58]. The utilized arguments in NbClust function included: scores of the supplied coordinates on the PCs as dataset, euclidean as the distance measure to be used to compute the dissimilarity matrix, k-means as the cluster analysis method to be used, silhouette as the index to be calculated. In k-means function, Hartigan-Wong was used as an algorithm for k-means calculations.

2.3.6 Free-Energy Analysis

The GaMD method facilitates unconstrained-enhanced sampling of a biomolecular system by adding a harmonic boost potential to smooth the system potential energy surface [26]. By constructing a harmonic boost potential that follows a Gaussian distribution, potential of mean force (PMF) (i.e., a free-energy profile) can be extracted by accurate reweighting of the GaMD simulations [26].

In the reweighting method, cumulant expansion can be used to approximate the ensemble-averaged Boltzmann factor, \({\langle {\text {e}}^{{\beta } {\Delta }V(r)}\rangle }\), where \({\beta } = \frac{1}{k_{\text {B}} T}\), \(k_{\text {B}}\) is Boltzmann constant, and T is the system absolute temperature [69]. To recover the most accurate free-energy profile, let \({\Delta }V(r)\) be the added non-negative boost energy to the system when the system potential is lower than a reference energy, where r denotes the atomic positions [69], and \({\langle {\text {e}}^{{\beta } {\Delta }V(r)}\rangle }_i\) be the ensemble-averaged Boltzmann factor of \({\Delta }V(r)\) for simulation frames found in the ith bin. Thus, the cumulant expansion to the third order is given by Eq. 2 [70].

$$\begin{aligned}&{\langle {\text {e}}^{{\beta } {\Delta }V(r)}\rangle }_i ~=~ \left[ \exp \left( \sum \limits _{k = 1}^{\infty } \dfrac{{\beta }^{k}}{k!} C_{k} \right) \right] _i \nonumber \\&=\left[ \exp \left( \beta C_{1} ~+~ \dfrac{{\beta }^{2}}{2} C_{2} ~+~ \dfrac{{\beta }^{3}}{6} C_{3} ~+~ \ldots \right) \right] _i \end{aligned}$$
(2)

where the first three cumulants can be calculated by

$$\begin{aligned}&C_{1}= {\langle {\Delta }V(r) \rangle }_i \end{aligned}$$
(3)
$$\begin{aligned}&C_{2} = {\langle {{\Delta }V^{2}(r)} \rangle }_i - {\langle {\Delta }V(r) \rangle }_i^{2} \equiv {\sigma }_{{\Delta }V(r)}^{2} \end{aligned}$$
(4)
$$\begin{aligned}&C_{3} = {\langle {{\Delta }V^{3}(r)} \rangle }_i - 3 {\langle {{\Delta }V^{2}(r)} \rangle }_i {\langle {\Delta }V(r) \rangle }_i+ 2 {\langle {\Delta }V(r) \rangle }_i^{3} \end{aligned}$$
(5)

where \(\sigma\) is the standard deviation of the \({\Delta }V(r)\) distribution in the ith bin. For a GaMD simulation of a biomolecular system, the probability distribution along a reaction coordinate A(r) is denoted as p[A(r)], which can be used to calculate the biased PMF, which is denoted as \(F^{\text {b}}[A(r)]\), for each bin i as illustrated in Eq. 6.

$$\begin{aligned} F_{i}^{\text {b}}[A(r)] ~=~ - \dfrac{1}{\beta } \ln \left\{ p_{i}[A(r)] \right\} \end{aligned}$$
(6)

Finally, the reweighted PMF, which is denoted as F[A(r)], can be evaluated by Eq. 7 for each bin i.

$$\begin{aligned} F_{i}[A(r)] ~=~ F^{\text {b}}_{i}[A(r)] ~-~ \dfrac{1}{\beta } \ln \left( {\langle {\text {e}}^{{\beta } {\Delta }V(r)}\rangle }_i \right) \end{aligned}$$
(7)

To identify distinct low-energy states of our biomolecule systems, free energy profiles were obtained by performing reweighting method along PC1 and PC2. To obtain a reasonable bin resolution, a bin width of 4.0 was used.

2.3.7 Pocket Druggability Prediction

The druggable pockets in the Arg175His mutant forms were predicted using the protein druggability prediction method provided in the PockDrug server [71]. After feeding the structure of the designated protein to the PockDrug server, the pockets on that protein were estimated on the basis of the amino acid atoms that form the surface of potential binding cavities [71]. The selected estimation method, which is called fpocket estimation method, extracted all the possible pockets from the protein surface using spheres of varying diameters, then prioritized these pockets for compound development in computer-aided drug design [71].

3 Results

3.1 Model Quality Assessment

The quality of our models, which have been constructed prior to the energy minimization processes, has been assessed using SWISS-MODEL server tools [72,73,74] and Structure Analysis and Verification Server tools [75,76,77,78,79]. Assessment results (Tables S1–S3 and Fig. S1) demonstrate through quality estimate, molprobity results, structure analysis, and verification server tools that the three models are reliable and can be studied via GaMD simulations.

3.2 Stability of Molecular Structures

The molecular structures of the wild-type and the Arg175His mutant forms are shown in Fig. S2. In general, the RMSD results of the p53-DBD structures (see Fig. S3) show acceptable domain stability throughout the production run time scale, and are consistent with RMSD results obtained from classical MD simulation [80]. On the other hand, the RMSD results of the full-length p53 forms (data not shown) have high values (in the range of \(5-20~{\AA }\)), which are attributed, as expected, to the free movements of both the p53-NTD and the p53-CTD [52]. Therefore, our next analyses are mainly focused on investigating the dynamics of p53-DBD forms in the presence of the p53-NTD and the p53-CTD.

The radius of gyration results of the p53-DBD structures (see Fig. S4) have steady values in all forms throughout the production run time scale. The steady values of the radius of gyration indicate acceptable stability in the p53-DBD folding state.

The RMSF results of the full-length p53 forms (see Fig. S5) confirm the high thermal fluctuations of the p53-NTD and the p53-CTD relative to the thermal fluctuations of the p53-DBD. As seen in Fig. S5, including the p53-NTD and the p53-CTD in the RMSF calculation will affect the RMSF values of the p53-DBD. On the other hand, RMSF results of only the p53-DBD forms (see Fig. 2) show changes in thermal fluctuations of the L1, \({\alpha }1\)–\({\beta }5\), and L3 loops as well as the \({\beta }6\)–\({\beta }7\) turn. These highlighted thermal fluctuations agree with the observed thermal fluctuations in the classical MD study [81]. In addition, it is observed that the \({\alpha }1\) helix in the middle of the L2 loop spontaneously unfolds in all simulations, and this observation is consistent with the observation in the classical MD study at \(300~\text {K}\) [51].

Fig. 2
figure 2

Root-mean-square fluctuation (RMSF) of the p53-DBD forms: (a) inactive; green, distal-active; red, proximal-active; black. (b) Distal-Arg175His mutant; red, proximal-Arg175His mutant; black. The location of the secondary structures are labeled (Color figure online).

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3.3 Dynamics of Protein Structures

Figure S6 shows the PCA scree plot, which indicates the proportion of variance against its mode index. The first two components together make up 45.4%, 20.4%, 29.5%, 38.2%, and 27.1% of the variance of the inactive, distal-active, proximal-active, distal-Arg175His mutant, and proximal-Arg175His mutant forms, respectively.

Most of the significant dynamics of p53-DBD forms can be captured by PC1 [65]; therefore, Figs. 3 and 4 show the porcupine plots of the PC1 obtained by performing PCA on GaMD trajectories of the p53-DBD forms.

Fig. 3
figure 3

Porcupine plot of the PC1 for the wild-type p53-DBD forms: (a) inactive, (b) distal-active, and (c) proximal-active. The arrows indicate direction of the eignvector and its magnitude in units of Å. Colors show the significant movements of the regions: orange, L1 loop; green, \({\alpha }1\)–\({\beta }5\) loop; red, \({\beta }6\)–\({\beta }7\) turn; magenta, \({\beta }7\)–\({\beta }8\) turn (Color figure online).

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Fig. 4
figure 4

Porcupine plot of the PC1 for the mutant p53-DBD forms: (a) distal-Arg175His mutant and (b) proximal-Arg175His mutant. The arrows indicate direction of the eignvector and its magnitude in units of Å. Colors show the significant movements of the regions: orange, L1 loop; red, \({\beta }6\)–\({\beta }7\) turn; magenta, \({\beta }7\)–\({\beta }8\) turn. The Arg175His mutation is depicted with CPK representation (Color figure online).

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In the inactive p53-DBD form, its dynamics illustrates drastic motions in the L1 loop as well as in the \({\beta }6\)–\({\beta }7\) and \({\beta }7\)–\({\beta }8\) turns (see Fig. 3a). On the other hand, the dynamics of the distal-active p53-DBD form contains moderate motions in the \({\alpha }1\)–\({\beta }5\) loop and the \({\beta }7\)–\({\beta }8\) turn (see Fig. 3b), whereas the dynamics of the proximal-active p53-DBD form embraces significant motions in the L1 loop as well as in the \({\alpha }1\)–\({\beta }5\) loop and the \({\beta }7\)–\({\beta }8\) turn (see Fig. 3c). In addition, the dynamics of the distal-Arg175His mutant form shows extreme motions in the L1 loop as well as in the \({\beta }6\)–\({\beta }7\) and \({\beta }7\)–\({\beta }8\) turns (see Fig. 4a), whereas the dynamics of the proximal-Arg175His mutant form exhibits moderate motions in the \({\beta }7\)–\({\beta }8\) turn (see Fig. 4b).

Projecting the trajectory frames onto the plane formed by PC1 and PC2 (see Fig. S7) reveals random diffusion in a high-dimensional harmonic potential. The observed patterns can be interpreted as thermal motion along a shallow free-energy landscape [82]. Even though the PCA is a powerful tool for finding global-correlated motions in atomic simulations of biomolecules, yet it does not partition the frames into distinct conformational states. Contrarily, conformational states analysis, which can be achieved by clustering the PC data, allows comparisons of all conformers sampled during the apparent thermal diffusion. By using the NbClust function [68] built in R language [58], the PC data of each form consists of two clusters (see Fig. 5). This observation is also supported by the cluster quality results (see Fig. S8), which show an identified kink at cluster count of two. In addition, Fig. 5 illustrates that approximately 50% of PCA time scale corresponds to cluster 1 in most p53-DBD forms.

Fig. 5
figure 5

Clustering results of k-means algorithm on subspace dimension projected on the 2D plane formed by the PC1 and PC2 of the p53-DBD forms: (a) inactive, (b) distal-active, (c) proximal-active, (d) distal-Arg175His mutant, and (e) proximal-Arg175His mutant.

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3.4 Free Energy Profiles

The free energy profiles of the p53-DBD forms are shown in Fig. 6. Clearly, the inactive p53-DBD form is confined to an energetic well (see Fig. 6a) that is lower than those for the distal-active and proximal-active p53-DBD forms (see Fig. 6b and c, respectively). In addition, the energetic well for the distal-active p53-DBD form (see Fig. 6b) is lower than that for the proximal-active p53-DBD form (see Fig. 6c). On the other hand, the distal-Arg175His mutant form is confined to a lower energetic well (see Fig. 6d) than that for the proximal-Arg175His mutant form (see Fig. 6e).

Fig. 6
figure 6

Two-dimensional free energy profiles along PC1 and PC2 calculated for the p53-DBD forms: (a) inactive, (b) distal-active, (c) proximal-active, (d) distal-Arg175His mutant, and (e) proximal-Arg175His mutant.

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3.5 Probable Druggable Pockets

Prediction of the protein ability to bind drug-like molecules with high affinity is an interesting approach that has been adopted in p53-based cancer therapies [25]. As seen in Fig. 5, there are two clusters for each Arg175His mutant form. Therefore, the most probable druggable pockets for each cluster are listed in Table S4. The first and the last frames of the GaMD trajectories have been extracted to represent cluster 1 and 2, respectively. Fig. 7 shows the probable druggable pockets on the mutant forms. Specifically, the probable druggable pocket on the distal or proximal Arg175His conformation, which has been constructed prior to the minimization processes, is shown in Fig. 7a, whereas the probable druggable pockets on each cluster of the Arg175His mutant forms are shown in Fig. 7b–e.

Fig. 7
figure 7

Probable druggable pockets in the Arg175His mutant p53-DBD forms: (a) prior minimization processes, (b) cluster 1; distal conformation, (c) cluster 2; distal conformation, (d) cluster 1; proximal conformation, (e) cluster 2; proximal conformation. Colored surfaces show pockets: blue, pocket 1; green, pocket 2; gold, pocket 3; violet, pocket 4. The Arg175His mutation is depicted with CPK representation, and \(\text {Zn}^{2+}\) atom is colored in red color (Color figure online).

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4 Discussion

It has been suggested that maintaining the stability of the \(\text {Zn}^{2+}\)-binding site decreases the thermal fluctuation of the L2 loop and prevents aggregation [51]. By maintaining the stability of \(\text {Zn}^{2+}\)-binding site, the structural and dynamical properties of the full-length human p53 as well as its interdomain interactions have been studied by the classical MD method at \(300~\text {K}\) for \(850~\text {ns}\) [52]. Another classical MD simulation, maintained the stability of the \(\text {Zn}^{2+}\)-binding site and used TIP3P water model, has been conducted on p53-DBD monomers to investigate the dynamics of the wild-type and some aggregating mutant forms, including the Arg175His mutant form, at \(310~\text {K}\) for \(500~\text {ns}\) [80].

In this work, we have conducted GaMD simulations with an OPC water model at physiological temperature and pH to study the dynamics of five full-length human p53 proteins, wild-type and Arg175His mutant forms, for \(200~\text {ns}\). The molecular structures of these forms are shown in Fig. S2 and the observed conformational changes are illustrated in Figs. 3, 4, 5. The noticeable conformational changes of the L1 loop in the inactive p53-DBD (see Fig. 3a), distal-active p53-DBD (see Fig. 3b), and distal-Arg175His mutant (see Fig. 3d) forms indicate high-conformational flexibility of the L1 loop [31, 42, 52, 81, 83, 84]. In a classical MD simulation [84], it has been reported that the L1 loop occupies two major conformational states; an extended and a recessed states, which are crucial for binding to DNA elements. In our simulations, a change in the conformational states of the L1 loop has been observed in two forms, proximal-active and distal-Arg175His mutant forms as shown in Fig. S9, where the extended conformation is represented by a distance of \({\approx }10~{\AA }\) and the recessed conformation is represented by a distance of \({\approx }25~{\AA }\). As seen in Fig. S9, the dominant L1 loop conformation in our simulation is the extended conformation. The observed thermal flexibility of the L1 loop can be quenched by forming hydrogen bonds between the backbone atoms of the L1 loop and the N-terminus atoms of the \({\alpha }2\) helix in the presence of a DNA element [81, 84,85,86].

Another dynamical feature that has been observed in p53-DBD forms is the thermal motion of the \({\alpha }1\)–\({\beta }5\) loop (part of the L2 loop) in the distal-active and proximal-active p53-DBD forms (see Fig. 3b and c, respectively). Our observations are consistent with those in an X-ray study [31] and other classical MD studies [51, 52, 81, 84]. The observed thermal flexibility of the \({\alpha }1\)–\({\beta }5\) loop can be stabilized in the presence of dimer-dimer interface [19, 81, 86].

Among the other important outcomes of our simulations is the dynamics of the \({\beta }6\)–\({\beta }7\) and \({\beta }7\)–\({\beta }8\) turns. The \({\beta }6\)–\({\beta }7\) turn has drastic motions in the inactive (see Fig. 3a) and distal-Arg175His mutant (see Fig. 4a) forms, whereas the \({\beta }7\)–\({\beta }8\) turn has various motion strengths in all p53-DBD forms (see Figs. 3 and 4). The observed dynamics of the \({\beta }6\)–\({\beta }7\) and \({\beta }7\)–\({\beta }8\) turns agrees with that in classical MD studies [42, 80, 81]. It has been reported [80] that the \({\beta }6\)–\({\beta }7\) turn exhibits two conformational states; open and closed states, which are related to the thermodynamic stability of the p53-DBD; the open state represents a destabilizing (or destabilized) state of the p53-DBD, whereas the closed state represents the stable state of the p53-DBD. Figs. S10 and S11 confirm the existence of these states in our simulations, where the closed state is represented by an Arg209CA–Asp259CA distance of \({\approx }13~{\AA }\) or an Arg209CZ–Asp259O distance of \({\approx }10~{\AA }\) and the open state is represented by an Arg209CA–Asp259CA distance of \({\approx }23~{\AA }\) or an Arg209CZ–Asp259O distance of \({\approx }20~{\AA }\). Furthermore, the inactive and proximal-active p53-DBD forms explore both the open and closed states of the \({\beta }6\)–\({\beta }7\) turn, whereas the distal-active p53-DBD form explores an intermediate state between the open and closed states. On the other hand, the distal-Arg175His mutant form explores both the open and closed states of the \({\beta }6\)–\({\beta }7\) turn, whereas the proximal-Arg175His mutant form explores the closed state. The observed thermal flexibility of the \({\beta }6\)–\({\beta }7\) turn can be quenched through formation of dimer-dimer interface [86] and hydrogen bonding with PRD region [52], whereas the thermal flexibility of the \({\beta }7\)–\({\beta }8\) turn can be stabilized by forming dimer-dimer interface [81, 86].

These remarkable dynamics can be partitioned into distinct conformational states by performing clustering analysis on the PC data [67]; thus, allowing comparisons of all conformers sampled during the apparent thermal diffusion. As seen in Fig. 5, the PC data of each form consists of two clusters (distinct conformations). The presence of two clusters in each p53-DBD form is worth investigation by other analysis techniques, such as free energy analysis (see Fig. 6). The shape of the plots in Fig. 6 resembles the shape of the plots in Figs. 5 and S7; therefore, these free energy profiles represent the energy of the conformational clusters. Consequently, the flatness of the energetic wells in the free energy profiles (see Fig. 6) probably means an easy process for the protein to undergo a conformational change from cluster 1 to cluster 2. In addition, it is observed that the distal forms have lower free-energy profiles than those of the proximal forms. This observation might indicate, in general, that the distal conformation is more thermally stable than the proximal conformation. The proximal conformation is stabilized by the presence of the DNA elements [19].

The p53-DBD contains a region called aggregation prone region (APR), spanning residues (251–257) within the \({\beta }9\) strand [32], which participates in the aggregation behavior of the Arg175His mutant [87]. Our results (see Fig. 2, 3, 4) show very stable APR with no significant dynamical behavior. In addition, the solvent accessible surface area (SASA) of the \({\beta }9\) strand has been calculated using Connolly surface area method [88] and is shown in Fig. S12. There is no significant difference between the SASA of the wild-type forms (see Fig. S12a) and that of the Arg175His mutant forms (see Fig. S12b), and this observation agrees with that in the classical MD simulations study [80]. The similarity of the SASA results, Fig. S12a and b, might be attributed to the maintained stability of the \(\text {Zn}^{2+}\)-binding site in our simulations. Therefore, it is not expected to see aggregation behavior of the Arg175His mutant forms in our simulations.

The most frequently mutated residues in the human p53 protein are at or near the p53-DNA interface, specifically, the 2 large loops and the loop-sheet-helix motif (the L1 loop, the \({\beta }2\)–\({\beta }2\)’turn, the 4 C-terminal residues of \({\beta }10\) strand, and the \({\alpha }2\) helix) [85, 89]. In the classical MD simulation study of Arg175His mutant [90], a hydrophobic patch has been suggested as a druggable site to prevent unfolding and aggregation by stabilizing the zinc binding region. On the basis of the two conformational Agr175His forms and the cluster states, we have predicted 7 druggable pockets on the Agr175His mutant forms (see Fig. 7b–e). These predicted pockets (Table S4) are different from the reported ones [80, 90]. To rule out the pseudo pockets, the probable druggable pockets on the active p53 forms are shown in Table S5 and Fig. S13. The pockets on the Agr175His forms (see Fig. 7a, c colored with yellow, and d) are expected to be pseudo pockets because they exist on the active p53 forms (see the blue colored pockets in Fig. S13a, b, and d). Moreover, the pocket on the Agr175His form (see Fig. 7b) is expected to be a pseudo pocket because it exists on the active p53 forms (see Fig. S13c and d colored with green). In addition, the pocket on the Agr175His form (see the violet colored pocket in Fig. 7c) is expected to be a pseudo pocket because it exists on the active p53 forms (see the yellow colored pocket in Fig. S13a). Consequently, there are three remaining pockets on the Agr175His form (see Fig. 7c colored with blue or green and e) that have to be clarified.

The two representative clusters of each Arg175His mutant forms are depicted with electrostatic potential surface (EPS) (see Fig. S14), whereas the EPS of the two representative clusters of each active p53-DBD forms are shown in Fig. S15. Clearly, there is more negative EPS and deeper cavity around the mutation point in the mutant forms than that in the active wild-type forms. Therefore, we expect that the pockets near the mutation point to have desirable docking affinity. Specifically, the first pocket in the Arg175His mutant forms (see the blue colored pockets in Fig. 7c and e) can be used in a drug screening study as one big pocket. Therefore, the blue colored pockets in Fig. 7c and e are the unique pockets that are expected to be the targeted pockets in a drug screening study.

5 Conclusions

The novel GaMD method has several applications in sampling biomolecular systems and free-energy calculations of biomolecules. Five full-length human p53 forms have been investigated by GaMD simulations in OPC water model at physiological temperature and pH. our observations, obtained throughout \(200~\text {ns}\) of production run, are in good agreement with the relavent results in the classical MD studies [52, 80, 84, 90]. Therefore, GaMD method is more economic and efficient method than the classical MD method for studying biomolecular systems.

The featured dynamics of the five human p53-DBD forms include noticeable conformational changes of the L1 and \({\alpha }1\)–\({\beta }5\) loops as well as the \({\beta }6\)–\({\beta }7\) and \({\beta }7\)–\({\beta }8\) turns. The observed thermal flexibility of these regions can be stabilized either by binding to DNA element or by forming dimer–dimer interface [19, 81, 84,85,86].

By a subsequent clustering analysis of the structural frames in the subspace spanned by PC1 and PC2, we have identified two clusters that represent two distinct conformational states. The free-energy profiles of these clusters in each p53-DBD form demonstrate the flexibility of the protein to undergo a conformational transition between the two clusters. However, the aggregation behavior of the Arg175His mutant forms is not expected to be observed because of the maintained stability of the \(\text {Zn}^{2+}\)-binding site in our simulations.

The utilized bonded approach for maintaining the \(\text {Zn}^{2+}\)-binding site in our simulation might be considered inappropriate technique for comparing the results of the wild-type and mutant forms of p53 protein. Therefore, we encourage using nonbonded approach for maintaining the \(\text {Zn}^{2+}\)-binding site by electrostatic and van der Waals interactions, which allow studying the catalytic function of the p53 protein for only a short period of simulation time scale [42].

By using a representative structure for each cluster of the Arg175His forms, we have predicted seven druggability pockets. Four druggability pockets on the Arg175His forms have been ruled out because there are similar pockets to them that exist in the active p53 forms. Furthermore, the druggability pockets near the mutated residue are expected to have high docking affinity because of the EPS influence. Consequently, the two druggability pockets near the mutation site are expected to be actual pockets, which will be helpful for the compound clinical progression studies.